×

zbMATH — the first resource for mathematics

Approximations of set-valued functions by metric linear operators. (English) Zbl 1123.26024
The authors adapt linear approximation operators for real-valued functions, based on samples of the approximated function, to set-valued functions by replacing an operation between numbers with an operation between sets. They introduce approximation operators for univariante set-valued functions with general compact images in \(\mathbb{R}^n\). Finally, as examples the authors study metric Bernstein operators, metric Schoenberg operators, and metric polynomial interpolants.

MSC:
26E25 Set-valued functions
54C65 Selections in general topology
PDF BibTeX XML Cite
Full Text: DOI arXiv